Secret sharing splits a secret into shares (which could be termed parts or pieces of the secret), and was invented by Adi Shamir and George Blakley, independently. The secret can be regenerated, using a sufficient subset (i.e., a specific threshold minimum number of shares or up to and including all) of the shares. Depending on the scheme used for secret sharing, a mathematical operation or algorithm is applied to a sufficient number (specific to the scheme) of the shares, parts or pieces of the secret to recover the secret. Secrets can be used in computing, communication and storage systems for encrypting and decrypting data or the secrets can act as passwords, keys for locks, or features for other security functions. For example, a secret (and each of the shares, parts or pieces of the secret) can be a binary number. In a distributed system, sending shares of a secret to different members of the system protects against theft of or from, or unauthorized access to any one member (or even a few members) of the system, which would at most result in theft of a share or a few shares, but not an entire key or enough shares to regenerate a key. Periodic generation of a new key is desirable from the standpoint of providing additional protection. However, it may not be possible to write a new secret to all of the members of a distributed system, because one or more members might be unavailable at the time the shares are written. If this happens, and the system fails, it is possible that a different set of system members will be available upon reboot of the system, in which case the new secret might not be recoverable, as the required quorum of shares for regenerating the secret might not be available. A distributed system facing such a condition might start again and re-split a secret, sending shares to available system members, whereupon the above situation could recur many times or indefinitely.
It is within this context that the embodiments arise.